Online log calculator tool to calculate logarithm of a given positive valve to the base e, base 10, base 2 or any base entered by the user.

The log calculator tool (logarithm calculator) allows you to calculate the logarithm of a positive real number with enetred base (positive, not equal to 1). You can enter any positive real number to find its logarithm, and enter the base value to solve the expression problem.

Logarithms appear in all sorts of calculations in engineering and science, business and economics. Before the days of calculators they were used to assist in the process of multiplication by replacing the operation of multiplication by addition. Similarly, they enabled the operation of division to be replaced by subtraction. They remain important in other ways, one of which is that they provide the underlying theory of the logarithm function. This has applications in many fields, for example, the decibel scale in acoustics.

Consider the expression 16 = 2^{4}.

Remember that 2 is the base, and 4 is the power. An alternative, yet equivalent, way of writing this expression is log_{2} 16 = 4. This is stated as 'log to base 2 of 16 equals 4’. We see that the logarithm is the same as the power or index in the original expression. It is the base in the original expression which becomes the base of the logarithm.

The two statements: 16 = 2^{4} and log_{2} 16 = 4 ;

are equivalent statements. If we write either of them, we are automatically implying the other.

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